Cold set morning tire pressure changes due to altitude changes are small and not worth messing with on my load E truck and trailer tires.
However higher altitudes can be colder which has a large effect on morning cold set tire pressures.
We pull up to Eagle Nest, NM (8500' elevation where we go) with 30 degree morning temps from NE OK where its 100-110 degrees. Tire pressure in the truck and trailer are always down 8-10 lbs in the mornings but when it warms up to 75-80 degrees tire pressure come back to normal pressure sitting in camp.